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I believe it works because it is used fairly close to your eyes (unlike a cinema screen) so that the angle of viewing of each eye is significantly different. It enables the display to present a different view to each eye so that it can give a stereo image. The screen is devised so that the left eye will not see the image intended for the right eye and vice versa. I must emphasise that I have not seen one or read any technical data on the device, but this is how I expect it works.
In fact a quick search on the web suggests that it uses a "parallax barrier" to do this:http://mediakick.org/2010/06/21/nintendo-3ds-how-it-works/